%I
%S 2501,123953,203482,204385,206197,304825,425273,568741,726193,727898,
%T 734738,906665,1119805,1124041,1334554,1341493,1346129,1565626,
%U 1568129,1570634,1573141,1578161,1580674,1583189,1590746,1593269,1828633,2126605,2138285,2144137
%N Numbers k such that the continued fraction for sqrt(k) has odd period and central terms 100.
%H Chai Wah Wu, <a href="/A031688/b031688.txt">Table of n, a(n) for n = 1..1000</a>
%t cf100Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1,1}, ContinuedFraction[ s][[2]]];len=Length[cf];OddQ[len] && cf[[(len+1)/2]] == 100]; Select[Range[2200000],cf100Q] (* _Harvey P. Dale_, May 29 2016 *)
%o (Python)
%o from sympy import continued_fraction_periodic
%o A031688_list = [n for n, s in ((i, continued_fraction_periodic(0,1,i)[1]) for i in range(1,10**5)) if isinstance(s, list) and len(s) % 2 and s[(len(s)1)//2] == 100] # _Chai Wah Wu_, Jun 11 2017
%K nonn
%O 1,1
%A _David W. Wilson_
%E Definition corrected and terms corrected and extended by _Harvey P. Dale_, May 29 2016
